Question

A solid iron rectangular block of dimensions 4.4 m, 2.6 m and 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe (in m).

• A. 112
• B. 221
• C. 121
• D. 211

Answer 1

The correct option is

B

112

Volume of iron
$=(440\times 260\times 100)c{m}^3$.

Internal radius of the pipe
$=30cm$.

External radius of the pipe
$=(30+5)cm=35cm$.

Let the length of the pipe be $hcm$.

Volume of iron in the pipe = (External volume) - (Internal volume)

$=\left[\pi \right(35{)}^2\times h-\pi (30{)}^2\times h]c{m}^3$

$=\left(\pi h\right)\left((35{)}^2-(30{)}^2\right)c{m}^3$

$=(65\times 5)\pi hc{m}^3$

Volume of iron in the pipe = Volume of iron block

$\Rightarrow \left(325\pi h\right)c{m}^3=440\times 260\times 100$

$h=\frac{440\times 260\times 100}{325}\times \frac{7}{22}cm$

$h=11200cm$

$h=\frac{11200}{100}=112m$

Hence, the length of the pipe is 112 m.